The velocity of sound in air at 15^{} {C} is 35400 {ms}^{-1}. Calculate the velocity at 47^{} {C}

Correct Answer is : 358ms−1358 {ms}^{-1}358ms−1

Correct Answer is : 358ms−1358 {ms}^{-1}358ms−1

Test Index

WAEC Physics 2020 Paper

Question : 22

Total: 51

15^{\circ} \mathrm{C}

35400 \mathrm{ms}^{-1}

47^{\circ} \mathrm{C}

Solution:

Concept:

Speed of sound in air is directly proportional to the square root of absolute temperature:

v \propto \sqrt{T}

Explanation:

15^\circ \mathrm{C}

, take the standard speed of sound as

v_1 = 340\ \mathrm{m\,s^{-1}}

The given value

35400\ \mathrm{m\,s^{-1}}

is a typographical error because the options are in the range of hundreds.

Convert temperatures to kelvin:

T_1 = 15 + 273 = 288\ \mathrm{K}

T_2 = 47 + 273 = 320\ \mathrm{K}

Using the relation:

\frac{v_2}{v_1} = \sqrt{\frac{T_2}{T_1}}

\frac{v_2}{340} = \sqrt{\frac{320}{288}} = \sqrt{\frac{10}{9}}

Therefore:

v_2 = 340 \times \sqrt{\frac{10}{9}}

v_2 = 340 \times 1.054 = 358\ \mathrm{m\,s^{-1}}

Answer:

v_2 = 358\ \mathrm{m\,s^{-1}}

, so the correct option is C.

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